Exercise 4.1 & 5.1

Nora Chirikure, Ziyu Lin, Felix Hüskes, Anton Bogs & Elias Koch

1 Collider Bias (4.1)

Declare a simple design in which

X and Y both have a positive effect on (binary) K but X does not cause Y
a researcher conditions on K == 1 when estimating the effect of X on Y

Show that this can generate biased results. Can you find situations where the bias can be either positive or negative?

1.1 DAG

1.2 How can the relationship between X and Y be changed?

1.2.1 K = rbinom(N, 1, prob = pnorm(X + Y))

1.2.2 K = rbinom(N, 1, prob = pnorm(X x Y))

1.2.3 K = rbinom(N, 1, prob = pnorm(X / Y))

2 Estimators (5.1)

Block	Treat	Outcome
1	0	0
1	0	0
1	1	1
2	0	0
2	0	0
2	0	1
2	1	0
2	1	1
2	1	1

2.1 Block-Wise Estimated Effects

2.2 ATE, ATT, ATU, DIM

2.3 Redesinging & Diagnosing the last Design